A college dean is interested in the exam performance of students in a biology course. After the final exam, students are randomly selected from three different section of the biology course. What can be conclude with an α of 0.05? The data are below.

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² =  ;  ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

At least on section differs on the final exam.None of the sections differ on the final exam.    

e) Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 2: difference =  ; significant:  ---Select--- Yes No
2 vs. 3: difference =  ; significant:  ---Select--- Yes No

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
2 vs. 3: test statistic =  ; significant:  ---Select--- Yes No
1 vs. 2: test statistic =  ; significant:  ---Select--- Yes No

An educational psychologist has developed a mediation technique to reduce anxiety. The psychologist selected a sample of high anxiety students that are asked to do the mediation at two therapy sessions a week apart. The participants' anxiety is measured the week before the first session and at each subsequent session. Below are the anxiety scores for the participants. What can the psychologist conclude with α = 0.01?

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² =  ;  ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

At least one of the sessions differ on anxiety.None of the sessions differ on anxiety.    

e) Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 3: difference =  ; significant:  ---Select--- Yes No
2 vs. 3: difference =  ; significant:  ---Select--- Yes No

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 3: test statistic =  ; significant:  ---Select--- Yes No
2 vs. 3: test statistic =  ; significant:  ---Select--- Yes No

Consider the following data for a dependent variable y and two independent variables, x₁and x₂.

Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary.

a. Develop an estimated regression equation relating y to x₁.

ŷ =  +  x₁

Predict y if x₁= 35.

ŷ =

b. Develop an estimated regression equation relating y to x₂.

ŷ =  +  x₂

Predict y if x₂= 25.

ŷ =

c. Develop an estimated regression equation relating y to x₁and x₂.

ŷ =  +  x1 +  x2

Predict y if x₁= 35 and x₂= 25.

ŷ =

A personnel director in a particular state claims that the mean annual income is greater in one of the​ state's counties​ (county A) than it is in another county​ (county B). In County​ A, a random sample of 1818 residents has a mean annual income of $ 40 comma 800$40,800 and a standard deviation of $ 8500$8500. In County​ B, a random sample of 88 residents has a mean annual income of $ 37 comma 700$37,700 and a standard deviation of $ 5500$5500. At alphaαequals=0.100.10​, answer parts​ (a) through​ (e). Assume the population variances are not equal. If​ convenient, use technology to solve the problem.

When using r programming or statistical software:

(A) From the summary, which variables seem useful for predicting changes in independent variable?

(B) For the purpose of variable selection, does the ANOVA table provide any useful information not already in the summary?

Why is it popular for advertisements to always state a confidence interval? Give an example of where you have seen this.

For small training sets variance may contribute more to the overall error than bias. Sometimes this is handled by reducing the complexity of the model, even if the model is too simple. Why do you suppose this is the case? Come up with your own example of this

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years.

To make sure the Excel regression package is installed.

Click “Tools”, à“Add-Ins” àchoose “Analysis Toolpak” and click “OK”.

To use the Excel regression package,                                                     

Click “Tools”, à“Data Analysis” and click “Regression”.

            a.   Use the method of least squares to compute an estimated regression line between sales and advertising.

            b.   If the company's advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars.

            c.   What does the slope of the estimated regression line indicate?

            d.   What is the coefficient of determination and fully interpret its meaning.

            e.  What is the standard error of the estimation?

            f.    Use the F test to determine whether or not the regression model is significant at a= 0.05.

            g.   Use the t test to determine whether the slope of the regression model is significant at a= 0.05.

            h.   Develop a 99% confidence interval for the slope of the regression model.

The prices of the 21​ top-rated 28-inch direct view television sets are as follows. ​$340 ​$410 ​$510 ​$620 ​$710 ​$810 ​$860 360 430 550 620 750 810 890 380 470 580 660 780 840 890 Determine Upper Q 2​, Upper Q 1​, and Upper Q 3.

Find the value of the standard normal random variable zz , called z0z0 such that:

(a) P(z≤z0)=0.9999P(z≤z0)=0.9999
z0=z0=

(b) P(−z0≤z≤z0)=0.922P(−z0≤z≤z0)=0.922
z0=z0=

(c) P(−z0≤z≤z0)=0.3954P(−z0≤z≤z0)=0.3954
z0=z0=

(d) P(z≥z0)=0.4497P(z≥z0)=0.4497
z0=z0=

(e) P(−z0≤z≤0)=0.3225P(−z0≤z≤0)=0.3225
z0=z0=

(f) P(−1.66≤z≤z0)=0.5474P(−1.66≤z≤z0)=0.5474
z0=z0=

The manager of a supermarket chain wants to determine if the location of the product - where it is to be displayed - has any effect on the sale of a pet toys. Three different aisle locations are to be considered: the front of the aisle, the middle of the aisle, or the rear-aisle. Twenty-one stores are randomly selected, with 7 stores randomly assigned to sell the pet toy at the front-aisle, the middle-aisle, and the rear-aisle.

Front Middle Rear

8.6 3.2 4.6 7.2 2.4 6.0 5.4 2.0 4.0 6.2 1.4 2.8 5.0 1.8 2.2 4.0 1.6 2.8 4.5 1.8 2.5

A boxplot of the data is provided as well as MINITAB output:

1. (a) Does this data indicate that the sales of the pet toy are the same at the three aisle locations? State the appropriate statistical hypotheses.

2. (b) To test the H0 in part (a), an ANOVA table was obtained in MINITAB:

        Source  DF     SS     MS      F      P
        Factor   2  51.59
        Error
        Total   20  80.82
   

   The P-value of test was found to be 0.000106.
   (i) Provide the value of the test statistic from which this P -value was found.

⃝c Jim Stallard 2019: Reproduction, in whole or in part, requires written consent of the copyright holder.6

(ii) Using a level of significance of 5%, what can you conclude from this data? Write a brief sentence describing your finding. [2]

(c) The output below results from an application of Tukey’s HSD method.

   Front subtracted from:

            Lower  Center   Upper   --+---------+---------+---------+-------
   Middle  -5.553  -3.814  -2.076   (------*------)
   Rear    -4.024  -2.286  -0.547         (------*------)

                                    --+---------+---------+---------+-------
                                   -5.0      -2.5       0.0       2.5

   Middle subtracted from:

          Lower  Center  Upper   --+---------+---------+---------+-------
   Rear  -0.210   1.529  3.267                        (------*------)

Summarize these results.

⃝c Jim Stallard 2019: Reproduction, in whole or in part, requires written consent of the copyright holder.4

MINITAB output:

Pearson correlation of MATScore and CalculusGrade = 0.840
Coefficients

Term       Coef  SD Coef  T-Value  P-Value
Constant  40.78     8.51     4.79    0.001
MATScore  0.766    0.175     4.38    0.002

⃝c Jim Stallard 2019: Reproduction, in whole or in part, requires written consent of the copyright holder.5

1. (a) From the scatterplot, what can you say about the relationship between a student’s math achievement

   test score and their Calculus I final grade?

2. (b) Letting a student’s math achievement test score be the predictor variable x and their Calculus I final grade by the response variable y, estimate the model that allows you to predict a student’s Calculus I final grade as a linear function of his/her math achievement test score.

3. (c) Find the coefficient of determination, and interpret its meaning.

4. (d) Does the data indicate that the y-intercept of the model can be removed or retained? Use a level of significance of 5%.

5. (e) Find a 95% confidence interval estimate for β1, and interpret its meanign. (Note: t0.025,df=8 = 2.306).

6. (f) Consider the following MINITAB output:

        Variable  Setting
        MATScore       70
   

            Fit   SE Fit        95% CI              95% PI
        94.3735  5.02118  (82.7946, 105.952)  (71.2024, 117.545)
   

   Find a 95% confidence interval that will predict the Calculus I final grade of a student who scored 70% on their math achievement test score.

To test whether students in a higher grade level will be less disruptive in class, a school psychologist records the number of documented interruptions during one day of classes from nine local high schools. The sample consisted of nine

(n = 9)

freshman, sophomore, junior, and senior high school classes. The data for each high school class are given in the table.

(a) Complete the F-table. (Round your answers to two decimal places.)

(b) Is it necessary to compute a post hoc test? Explain. (Assume alpha equal to 0.05.)

Yes, post hoc analyses are appropriate because the ANOVA is significant.

No, post hoc analyses are not appropriate because the ANOVA is not significant.    

You may need to use the appropriate table in Appendix B to answer this question.

Motor-Dexterity Test Motor-dexterity tests are often used in psychological studies, especially in neuropsychology. For this task, we are going to test motor-dexterity while looking for signs of frustration. First, take a clean pair of rolled-up socks or some other soft item. Then, have the participants throw it into a hoop you make with your arms. The objective is not to see how well they do the task but to see which hand they use; you are trying to determine dominance. After doing this task, ask the participants which hand they prefer to use when writing. While most will prefer the right, some will prefer the left. If a person says both, ask that individual to write a sentence with both hands, one at a time and the two of you can decide which hand to call dominant. In most cases, people will report they use the right hand more, and they will also unintentionally pick the right hand to throw the object with. If they report left and use the right hand to throw, then record that as mixed, but select the hand they choose as dominant. In the end, you will go with what the participant decides. You are required to record all information on the data sheet. This study involved ten participants. The researcher timed how fast each person put fifteen toothpicks into a mug with each hand. To reduce a significant difference being caused by practice effects, five of the participants started with their dominant hand (DH) and the next set of five started with their nondominant hand (NDH). While they were doing the task, the researcher rated the level of frustration while performing with one hand and then the other one. The researcher was careful not to allow experimenter bias to influence what he or she recorded. Here is the scale used to rate frustration: Very Frustrated Not Very Frustrated 5 4 3 2 1 Look at the data sheet: Participant # Start with NDH (seconds) FL-NDH DH (seconds) FL-DH 1 Right 7 3 6 1 2 Right 10 4 8 2 3 Right 9 3 8 2 4 Left 6 2 7 3 5 Right 8 4 6 1 6 Left 12 5 9 1 7 Left 8 1 7 1 8 Right 11 3 10 2 9 Left 8 2 8 2 10 Left 13 5 9 3 The hypotheses for the study were: People will perform the motor-dexterity task faster with their DH as compared to their NDH. People will show more frustration while using the NDH. Determine the average time with the motor-dexterity test, along with the standard deviation, and then use Minitab to analyze the data with a paired t-test to see if there is a significant performance difference between the two hands. Run another paired t-test to see if there is a difference in frustration (FL) while using the DH versus the NDH. Obtain the results and decide if the hypotheses are supported. Write a summary of the findings. Submit the results and summary of the findings in a 3- to 4-page Microsoft Word document.

Iconic memory is a type of memory that holds visual information for about half a second (0.5 seconds). To demonstrate this type of memory, participants were shown three rows of four letters for 50 milliseconds. They were then asked to recall as many letters as possible, with a 0-, 0.5-, or 1.0-second delay before responding. Researchers hypothesized that longer delays would result in poorer recall. The number of letters correctly recalled is given in the table.

(a) Complete the F-table. (Round your values for MS and F to two decimal places.)

(b) Compute Tukey's HSD post hoc test and interpret the results. (Assume alpha equal to 0.05. Round your answer to two decimal places.)

The critical value is_____ for each pairwise comparison.

Which of the comparisons had significant differences? (Select all that apply.)

-Recall following no delay was significantly different from recall following a half second delay.

-The null hypothesis of no difference should be retained because none of the pairwise comparisons demonstrate a significant difference.

-Recall following a half second delay was significantly different from recall following a one second delay.

-Recall following no delay was significantly different from recall following a one second delay.